Covering Points of a Digraph with Point-Disjoint Paths and Its Application to Code Optimization

Boesch, Francis T.; Gimpel, James F.

doi:10.1145/322003.322005

Cited by 73 publications

(36 citation statements)

References 4 publications

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“…It is worth to mention that even though the condition nd(H) = |H| may seem very restrictive this class of graphs contains for example paths P k for k ≥ 4 and cycles C k for k ≥ 5. Applications of the Partition into H problem with H being a path may be found in code optimization [2]. We say that a graph H is a prime graph if H fulfills the condition nd(H) = |H|.…”

Section: Theorem 13 For Any Fixed Graph H With Nd(h) = |H| and A Grmentioning

confidence: 99%

Partitioning Graphs into Induced Subgraphs

Knop

2017

Language and Automata Theory and Applications

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We study the Partition into H problem from the parameterized complexity point of view. In the Partition into H problem the task is to partition vertices of a graph G into sets V 1 , V 2 , . . . , V n such that the graph H is isomorphic to the subgraph of G induced by each set V i for i = 1, 2, . . . , n. The pattern graph H is fixed.For the parametrization we consider three distinct structural parameters of the graph Gnamely the tree-width, the neighborhood diversity, and the modular-width. For the parametrization by the neighborhood diversity we obtain an FPT algorithm for every graph H. For the parametrization by the tree-width we obtain an FPT algorithm for every connected graph H. Finally, for the parametrization by the modular-width we derive an FPT algorithm for every prime graph H.

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Section: Theorem 13 For Any Fixed Graph H With Nd(h) = |H| and A Grmentioning

confidence: 99%

Partitioning Graphs into Induced Subgraphs

Knop

2017

Language and Automata Theory and Applications

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“…Let G be a graph, D G be the DAG associated to G, and let Step (ii) computes a minimum path cover in the transitive DAG D G ; the problem is known to be polynomially solvable, since it can be reduced to the maximum matching problem in a bipartite graph formed from the transitive DAG [1]. The maximum matching problem in a bipartite graph takes O((m + n) √ n) time, due to an algorithm by Hopcroft and Karp [8].…”

Section: Proposition 3 Let G Be a Graph And Let D G Be The Dag Assocmentioning

confidence: 99%

Colinear Coloring on Graphs

Ioannidou

Nikolopoulos

2009

WALCOM: Algorithms and Computation

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Abstract. Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology, and the framework through which it was studied, we introduce the colinear coloring on graphs. We provide an upper bound for the chromatic number χ(G), for any graph G, and show that G can be colinearly colored in polynomial time by proposing a simple algorithm. The colinear coloring of a graph G is a vertex coloring such that two vertices can be assigned the same color, if their corresponding clique sets are associated by the set inclusion relation (a clique set of a vertex u is the set of all maximal cliques containing u); the colinear chromatic number λ(G) of G is the least integer k for which G admits a colinear coloring with k colors. Based on the colinear coloring, we define the χ-colinear and α-colinear properties and characterize known graph classes in terms of these properties.

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“…In that case, the result from MPCP is also the result for MWPCP in a unit-edge-weight graph, because the minimum number of paths implies the maximum number of edges. The MPCP is NP-hard (Boesch and Gimpel, 1977). When antiparallel edges are not allowed, i.e., directed edges .i; j / and .j; i / do not co-exist, there are approximation algorithms for MWPCP that have been studied (Moran et al, 1990).…”

Section: From Ancestral Adjacency To Ancestral Gene Ordermentioning

confidence: 99%

DUPCAR: Reconstructing Contiguous Ancestral Regions with Duplications

Raney

Suh

et al. 2008

Journal of Computational Biology

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Accurately reconstructing the large-scale gene order in an ancestral genome is a critical step to better understand genome evolution. In this paper, we propose a heuristic algorithm, called DUPCAR, for reconstructing ancestral genomic orders with duplications. The method starts from the order of genes in modern genomes and predicts predecessor and successor relationships in the ancestor. Then a greedy algorithm is used to reconstruct the ancestral orders by connecting genes into contiguous regions based on predicted adjacencies. Computer simulation was used to validate the algorithm. We also applied the method to reconstruct the ancestral chromosome X of placental mammals and the ancestral genomes of the ciliate Paramecium tetraurelia.

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Covering Points of a Digraph with Point-Disjoint Paths and Its Application to Code Optimization

Cited by 73 publications

References 4 publications

Partitioning Graphs into Induced Subgraphs

Partitioning Graphs into Induced Subgraphs

Colinear Coloring on Graphs

DUPCAR: Reconstructing Contiguous Ancestral Regions with Duplications

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